Abstract
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in the setting of Hilbert spaces. By using well-known Fan-KKM lemma, we derive the existence and uniqueness of a solution of the auxiliary problem for GEP. On account of this result and Nadler's theorem, we propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping.
| Original language | English |
|---|---|
| Pages (from-to) | 487-502 |
| Number of pages | 16 |
| Journal | Journal of Global Optimization |
| Volume | 43 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2009 |
Bibliographical note
Funding Information:Acknowledgements In this research, first author was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), and Science and Technology Commission of Shanghai Municipality grant (075105118).
Keywords
- Fixed points
- Generalized equilibrium problem
- Nonexpansive mappings
- Strong convergence
- Viscosity approximation method
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics